Subgroups — #33978953

Order 18688.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623894	C₂	1	1	yes	maximal, characteristic
2	Q₈×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622982	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622960	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622743	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622669	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622045	C₂	1	2	yes	maximal, complemented
8	#22622015	C₂	1	2	yes	maximal, complemented
9	#22621809	C₂	1	1	yes	maximal, characteristic, complemented
10	#22621757	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₁₆×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
12	SD₁₆×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#22621504	C₂	1	2	yes	maximal, complemented
14	#22621444	C₂	1	2	yes	maximal, complemented
15	#22621304	C₂	1	1	yes	maximal, characteristic, complemented
16	#22621267	C₂	1	2	yes	maximal, complemented
17	#22620932	C₂	1	2	yes	maximal, complemented
18	#22620889	C₂	1	1	yes	maximal, characteristic, complemented
19	#22620107	C₂	1	2	yes	maximal, complemented
20	#22619403	C₂	1	1	yes	maximal, characteristic, complemented
21	#464×D₇₃	C₂	1	2	yes	maximal, complemented
22	#22619052	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556622	C₂²	1	2	yes	complemented
25	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	complemented
26	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
27	#17989322	C₂²	1	1	yes	characteristic
28	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
29	#17989315	—	2	1	no	—
30	#17989315	C₂²	1	1	yes	characteristic, complemented
31	#17989307	C₂²	1	1	yes	characteristic
32	#17989302	—	2	1	no	—
33	#17989297	—	2	1	no	—
34	#17989297	C₂²	1	1	yes	characteristic
35	#17989292	—	2	2	no	—
36	#17989292	C₂²	1	2	yes	complemented
37	#17989262	—	2	2	no	—
38	Q₈×D₂₉₂	C₂²	1	1	yes	characteristic
39	Q₈×D₂₉₂	C₂²	1	1	yes	characteristic
40	Q₈×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
41	#17989247	C₂²	1	2	yes	—
42	#17989234	C₂²	1	2	yes	—
43	#17989233	—	2	1	no	—
44	D₄×D₂₉₂	C₂²	1	1	yes	characteristic
45	#17989208	—	2	1	no	—
46	#17989173	—	2	2	no	—
47	#17989144	—	2	1	no	—
48	#17989144	C₂²	1	1	yes	characteristic, complemented
49	#17989141	—	2	2	no	—
50	#17989141	C₂²	1	2	yes	complemented
51	#17989137	C₂²	1	1	yes	characteristic
52	#17989122	C₂²	1	2	yes	—
53	#124×D₇₃	C₂²	1	2	yes	—
54	#17989061	—	2	1	no	—
55	C₄×#11924028	—	2	1	no	—
56	C₄×#11924028	C₂²	1	1	yes	characteristic
57	C₄×Q₈×D₇₃	C₂²	1	2	yes	complemented
58	#17988980	C₂²	1	2	yes	complemented
59	#17988978	C₂²	1	2	yes	—
60	#17988967	C₂²	1	1	yes	characteristic, complemented
61	#17988960	C₂²	1	1	yes	characteristic
62	#17988948	C₂²	1	2	yes	complemented
63	#17988945	C₂²	1	2	yes	—
64	#17988938	C₂²	1	1	yes	characteristic, complemented
65	#17988934	C₂²	1	1	yes	characteristic
66	#17988924	C₂²	1	2	yes	complemented
67	#17988907	C₂²	1	2	yes	—
68	#17988891	C₂²	1	2	yes	complemented
69	#17988882	C₂²	1	1	yes	characteristic, complemented
70	#17988877	C₂²	1	1	yes	characteristic
71	#17988871	C₂²	1	2	yes	complemented
72	#17988866	C₂²	1	2	yes	complemented
73	#17988843	C₂²	1	2	yes	complemented
74	#17988831	C₂²	1	2	yes	—
75	#17988829	C₂²	1	2	yes	complemented
76	#17988827	C₂²	1	2	yes	complemented
77	#17988819	C₂²	1	2	yes	—
78	#17988817	C₂²	1	2	yes	—
79	#17988812	C₂²	1	2	yes	complemented
80	#17988811	C₂²	1	2	yes	complemented
81	#17988810	C₂²	1	2	yes	complemented
82	#17988810	C₂²	1	2	yes	complemented
83	#17988809	C₂²	1	2	yes	complemented
84	#17988809	C₂²	1	2	yes	complemented
85	#17988808	C₂²	1	2	yes	—
86	#17988807	C₂²	1	2	yes	—
87	#17988806	C₂²	1	2	yes	—
88	#17988797	C₂²	1	1	yes	characteristic, complemented
89	#17988797	C₂²	1	1	yes	characteristic, complemented
90	#17988797	C₂²	1	1	yes	characteristic, complemented
91	#17988796	C₂²	1	2	yes	complemented
92	#17988792	C₂²	1	1	yes	characteristic
93	#17988791	C₂²	1	2	yes	complemented
94	#17988787	C₂²	1	1	yes	characteristic
95	#17988787	C₂²	1	1	yes	characteristic
96	#17988751	C₂²	1	2	yes	complemented
97	#17988751	C₂²	1	2	yes	complemented
98	#17988744	C₂²	1	2	yes	complemented
99	#17988744	C₂²	1	2	yes	complemented
100	#17988741	C₂²	1	2	yes	complemented
101	#17988739	C₂²	1	2	yes	—
102	#17988736	C₂²	1	2	yes	—
103	#17988727	C₂²	1	2	yes	—
104	#17988717	C₂²	1	1	yes	characteristic, complemented
105	#17988717	C₂²	1	1	yes	characteristic, complemented
106	#17988693	C₂²	1	2	yes	complemented
107	#17988691	C₂²	1	2	yes	complemented
108	#17988690	C₂²	1	2	yes	complemented
109	#17988686	C₂²	1	2	yes	complemented
110	#17988661	C₂²	1	2	yes	complemented
111	#17988661	C₂²	1	2	yes	complemented
112	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
113	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
114	#17988643	C₂²	1	2	yes	complemented
115	#17988611	C₂²	1	1	yes	characteristic, complemented
116	C₄⋊C₈×D₇₃	C₂²	1	2	yes	complemented
117	#17988586	C₂²	1	2	yes	complemented
118	#103×D₇₃	C₂²	1	2	yes	complemented
119	#102×D₇₃	C₂²	1	2	yes	—
120	#529×C₇₃	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#483×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#480×C₇₃	C₂²	1	1	yes	characteristic
124	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#464×C₇₃	C₂²	1	1	yes	characteristic
127	#464×C₇₃	C₂²	1	1	yes	characteristic
128	#451×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#448×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
134	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924028	D₄	1	1	yes	characteristic
136	C₂×#11924028	C₂³	1	2	yes	—
137	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
138	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
139	C₂²×D₂₉₂	—	2	1	no	—
140	C₂×D₄×D₇₃	C₂³	1	2	yes	—
141	#14556622	—	4	4	no	—
142	C₂×Dic₂₉₂	C₂³	1	2	yes	—
143	C₂×Dic₂₉₂	C₂³	1	2	yes	—
144	C₂×#11924018	C₂³	1	2	yes	—
145	C₂×#11924018	C₂³	1	2	yes	—
146	C₂×#11924018	C₂³	1	2	yes	—
147	Q₁₆×D₇₃	—	4	4	no	—
148	C₂×#11924017	C₂³	1	2	yes	—
149	C₂×#11924017	C₂³	1	2	yes	—
150	C₂×#11924016	C₂³	1	2	yes	—
151	C₂×#11924015	C₂³	1	2	yes	—
152	C₂×#11924015	C₂³	1	2	yes	—
153	SD₁₆×D₇₃	—	4	4	no	—
154	C₂×#11924012	C₂³	1	2	yes	—
155	C₂×C₈×D₇₃	C₂³	1	2	yes	—
156	C₂×C₈×D₇₃	C₂³	1	2	yes	—
157	#14556591	—	2	1	no	—
158	#14556591	—	2	1	no	—
159	#14556591	—	2	1	no	—
160	#14556591	C₂³	1	1	yes	characteristic
161	#14556591	C₂³	1	1	yes	characteristic
162	#14556591	C₂³	1	1	yes	characteristic
163	#14556590	—	2	2	no	—
164	#14556590	C₂³	1	2	yes	—
165	#14556589	—	2	2	no	—
166	#14556589	C₂³	1	2	yes	—
167	#14556588	C₂³	1	1	yes	characteristic
168	#14556586	—	2	2	no	—
169	#14556584	—	2	2	no	—
170	#14556583	—	2	1	no	—
171	#14556583	—	2	1	no	—
172	#14556583	—	2	1	no	—
173	#14556581	—	2	2	no	—
174	#14556581	—	2	2	no	—
175	#14556581	—	2	2	no	—
176	#14556580	C₂³	1	2	yes	—
177	#14556579	—	2	1	no	—
178	#14556579	C₂³	1	2	yes	—
179	#14556578	C₂³	1	2	yes	—
180	#14556577	—	2	2	no	—
181	#14556577	—	2	2	no	—
182	#14556577	—	2	2	no	—
183	#14556576	—	2	2	no	—
184	#14556576	—	2	2	no	—
185	#14556573	—	2	2	no	—
186	#14556571	—	2	2	no	—
187	#14556571	—	2	2	no	—
188	#14556571	C₂³	1	2	yes	—
189	#14556571	C₂³	1	2	yes	—
190	#14556570	—	2	1	no	—
191	#14556570	—	2	2	no	—
192	#14556570	—	2	2	no	—
193	#14556570	—	2	1	no	—
194	#14556570	C₂³	1	2	yes	—
195	#14556569	—	2	2	no	—
196	#14556569	—	2	2	no	—
197	#14556569	—	2	2	no	—
198	#14556569	—	2	2	no	—
199	#14556567	—	2	2	no	—
200	#14556567	C₂³	1	2	yes	—
201	#14556566	C₂³	1	2	yes	—
202	#14556565	—	2	1	no	—
203	#14556565	—	2	1	no	—
204	#14556565	—	2	1	no	—
205	#14556564	—	2	2	no	—
206	#14556562	—	2	2	no	—
207	#14556561	—	2	2	no	—
208	#14556559	—	2	2	no	—
209	Q₈×Dic₇₃	C₂³	1	2	yes	—
210	C₄×Dic₁₄₆	—	2	1	no	—
211	C₄×Dic₁₄₆	—	2	1	no	—
212	C₄×Dic₁₄₆	—	2	2	no	—
213	C₄×Dic₁₄₆	—	2	2	no	—
214	C₄×Dic₁₄₆	—	2	1	no	—
215	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
216	C₄×Dic₁₄₆	C₂³	1	2	yes	—
217	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
218	#14556556	—	2	2	no	—
219	#14556556	C₂³	1	2	yes	—
220	#14556556	C₂³	1	2	yes	—
221	C₄×D₂₉₂	—	2	1	no	—
222	C₄×D₂₉₂	—	2	1	no	—
223	C₄×D₂₉₂	—	2	1	no	—
224	C₄×D₂₉₂	—	2	1	no	—
225	C₄×D₂₉₂	—	2	1	no	—
226	C₄×D₂₉₂	—	2	1	no	—
227	C₄×D₂₉₂	D₄	1	1	yes	characteristic
228	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
229	#14556553	—	2	2	no	—
230	#14556553	—	2	2	no	—
231	#14556553	C₂³	1	2	yes	—
232	C₄×C₂²⋊D₇₃	—	2	2	no	—
233	C₄×C₂²⋊D₇₃	—	2	2	no	—
234	C₄×C₂²⋊D₇₃	D₄	1	2	yes	—
235	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
236	#14556550	—	2	1	no	—
237	#14556550	—	2	1	no	—
238	#14556550	D₄	1	1	yes	characteristic
239	#14556549	—	2	2	no	—
240	#14556548	—	2	2	no	—
241	#14556548	D₄	1	2	yes	—
242	C₄⋊C₄×D₇₃	—	2	2	no	—
243	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₂²⋊C₄×D₇₃	—	2	2	no	—
246	C₂²⋊C₄×D₇₃	—	2	2	no	—
247	C₄²×D₇₃	—	2	2	no	—
248	C₄²×D₇₃	C₂³	1	2	yes	—
249	#14556524	C₂³	1	2	yes	—
250	#14556522	C₂³	1	2	yes	—
251	C₄⋊#10596831	C₂³	1	1	yes	characteristic
252	C₄⋊#10596831	C₂³	1	1	yes	characteristic
253	C₄⋊#10596831	C₂³	1	2	yes	—
254	#14556520	C₂³	1	2	yes	—
255	#14556520	C₂³	1	2	yes	—
256	#14556516	C₂³	1	2	yes	—
257	#14556516	C₂³	1	2	yes	—
258	#14556515	C₂³	1	2	yes	—
259	#14556514	C₂³	1	2	yes	—
260	#14556514	C₂³	1	2	yes	—
261	#14556514	C₂³	1	2	yes	—
262	#14556514	C₂³	1	2	yes	—
263	#14556513	C₂³	1	2	yes	—
264	#14556513	C₂³	1	2	yes	—
265	#14556512	C₂³	1	2	yes	—
266	#14556511	C₂³	1	2	yes	—
267	#14556511	C₂³	1	2	yes	—
268	#14556503	C₂³	1	2	yes	—
269	#14556503	C₂³	1	2	yes	—
270	#14556501	C₂³	1	2	yes	—
271	#14556501	C₂³	1	2	yes	—
272	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
273	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
277	#126×C₇₃	—	2	1	no	—
278	#125×C₇₃	C₂³	1	1	yes	characteristic
279	#124×C₇₃	C₂³	1	1	yes	characteristic
280	#123×C₇₃	—	2	1	no	—
281	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
282	#121×C₇₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₇₃	—	2	1	no	—
284	C₄×Q₈×C₇₃	—	2	1	no	—
285	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₇₃	—	2	1	no	—
291	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
292	#117×C₇₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₇₃	—	2	1	no	—
296	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
297	#107×C₇₃	C₂³	1	1	yes	characteristic
298	#107×C₇₃	C₂³	1	1	yes	characteristic
299	#106×C₇₃	C₂³	1	1	yes	characteristic
300	#106×C₇₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#103×C₇₃	C₂³	1	1	yes	characteristic
305	#103×C₇₃	C₂³	1	1	yes	characteristic
306	#103×C₇₃	C₂³	1	1	yes	characteristic
307	#103×C₇₃	C₂³	1	1	yes	characteristic
308	#103×C₇₃	C₂³	1	1	yes	characteristic
309	#102×C₇₃	C₂³	1	1	yes	characteristic
310	#102×C₇₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
315	C₂³×D₇₃	—	2	2	no	—
316	#11924028	—	2	4	no	—
317	#11924028	—	4	2	no	—
318	#11924028	—	4	2	no	—
319	C₂×Dic₁₄₆	—	2	2	no	—
320	C₂×Dic₁₄₆	—	2	1	no	—
321	C₂×Dic₁₄₆	—	2	2	no	—
322	C₂×Dic₁₄₆	—	2	2	no	—
323	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
324	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
325	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
326	Q₈×D₇₃	—	2	4	no	—
327	Q₈×D₇₃	—	4	2	no	—
328	Q₈×D₇₃	—	4	2	no	—
329	Q₈×D₇₃	—	4	2	no	—
330	C₂×D₂₉₂	—	2	2	no	—
331	C₂×D₂₉₂	—	2	1	no	—
332	C₂×D₂₉₂	—	2	1	no	—
333	C₂×D₂₉₂	—	4	4	no	—
334	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
335	C₂×D₂₉₂	C₂⁴	1	2	yes	—
336	C₂×C₂²⋊D₇₃	—	2	2	no	—
337	C₂×C₂²⋊D₇₃	—	2	2	no	—
338	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
339	D₄×D₇₃	—	4	2	no	—
340	D₄×D₇₃	—	4	2	no	—
341	C₂×C₄×D₇₃	—	2	2	no	—
342	C₂×C₄×D₇₃	—	2	2	no	—
343	C₂×C₄×D₇₃	—	2	2	no	—
344	C₂×C₄×D₇₃	—	2	2	no	—
345	C₂×C₄×D₇₃	—	2	2	no	—
346	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
347	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
348	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
349	Dic₂₉₂	—	4	2	no	—
350	Dic₂₉₂	—	4	2	no	—
351	#11924018	—	2	4	no	—
352	#11924018	—	4	2	no	—
353	#11924018	—	4	2	no	—
354	#11924017	—	4	2	no	—
355	#11924017	—	4	2	no	—
356	#11924016	—	4	2	no	—
357	#11924015	—	2	4	no	—
358	#11924015	—	4	2	no	—
359	#11924012	—	4	2	no	—
360	C₂×#10596831	C₂⁴	1	2	yes	—
361	C₂×#10596831	C₂⁴	1	2	yes	—
362	C₈×D₇₃	—	4	2	no	—
363	C₈×D₇₃	—	4	2	no	—
364	C₄⋊Dic₇₃	—	2	1	no	—
365	C₄⋊Dic₇₃	—	2	1	no	—
366	C₄⋊Dic₇₃	—	2	1	no	—
367	C₄⋊Dic₇₃	—	2	1	no	—
368	C₄⋊Dic₇₃	—	2	1	no	—
369	C₄⋊Dic₇₃	—	2	2	no	—
370	C₄⋊Dic₇₃	—	2	2	no	—
371	C₄⋊Dic₇₃	—	2	2	no	—
372	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
373	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
374	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
375	#11924007	—	2	2	no	—
376	#11924007	—	2	2	no	—
377	#11924007	—	2	2	no	—
378	#11924007	—	2	2	no	—
379	#11924007	—	2	2	no	—
380	#11924007	—	2	2	no	—
381	#11924007	—	2	2	no	—
382	#11924007	—	2	2	no	—
383	#11924007	—	2	2	no	—
384	#11924007	C₂×D₄	1	2	yes	—
385	#11924007	C₂×D₄	1	2	yes	—
386	C₂²⋊Dic₇₃	—	2	2	no	—
387	C₂²⋊Dic₇₃	—	2	2	no	—
388	C₂²⋊Dic₇₃	—	2	2	no	—
389	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
390	#11924005	—	2	2	no	—
391	#11924005	—	2	2	no	—
392	#11924005	—	2	2	no	—
393	#11924005	—	2	2	no	—
394	#11924005	—	2	2	no	—
395	#11924005	—	2	2	no	—
396	#11924005	—	2	2	no	—
397	#11924005	—	2	2	no	—
398	#11924005	—	2	2	no	—
399	#11924005	C₂×D₄	1	2	yes	—
400	#11924005	C₂×D₄	1	2	yes	—
401	C₄×Dic₇₃	—	2	2	no	—
402	C₄×Dic₇₃	—	2	2	no	—
403	C₄×Dic₇₃	—	2	2	no	—
404	C₄×Dic₇₃	—	2	2	no	—
405	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
406	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
407	C₄×Dic₇₃	C₂⁴	1	2	yes	—
408	C₂×Q₈×C₇₃	—	2	1	no	—
409	C₂×Q₈×C₇₃	—	2	2	no	—
410	C₂×Q₈×C₇₃	—	4	1	no	—
411	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
412	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
413	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
414	C₂×D₄×C₇₃	—	2	1	no	—
415	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₇₃	—	2	1	no	—
417	C₂²×C₄×C₇₃	—	2	1	no	—
418	C₂²×C₄×C₇₃	—	2	1	no	—
419	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
422	Q₁₆×C₇₃	—	2	2	no	—
423	Q₁₆×C₇₃	—	4	1	no	—
424	SD₁₆×C₇₃	—	2	2	no	—
425	SD₁₆×C₇₃	—	4	1	no	—
426	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
429	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₄⋊C₄×C₇₃	—	2	1	no	—
431	C₄⋊C₄×C₇₃	—	2	1	no	—
432	C₄⋊C₄×C₇₃	—	2	1	no	—
433	C₄⋊C₄×C₇₃	—	2	1	no	—
434	C₄⋊C₄×C₇₃	—	2	1	no	—
435	C₄⋊C₄×C₇₃	—	2	1	no	—
436	C₄⋊C₄×C₇₃	—	2	1	no	—
437	C₄⋊C₄×C₇₃	—	2	1	no	—
438	C₄⋊C₄×C₇₃	—	2	1	no	—
439	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₇₃	—	2	1	no	—
444	C₂²⋊C₄×C₇₃	—	2	1	no	—
445	C₂²⋊C₄×C₇₃	—	2	1	no	—
446	C₂²⋊C₄×C₇₃	—	2	1	no	—
447	C₂²⋊C₄×C₇₃	—	2	1	no	—
448	C₄²×C₇₃	—	2	1	no	—
449	C₄²×C₇₃	—	2	1	no	—
450	C₄²×C₇₃	—	2	1	no	—
451	C₄²×C₇₃	—	2	1	no	—
452	C₄²×C₇₃	—	2	1	no	—
453	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
456	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
457	C₂³×C₇₃	—	2	1	no	—
458	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
459	C₂²×D₇₃	—	2	2	no	—
460	C₂²×D₇₃	—	4	4	no	—
461	C₂²×D₇₃	—	8	2	no	—
462	C₂²×D₇₃	—	8	2	no	—
463	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
464	Q₈×C₇₃	—	2	1	no	—
465	Q₈×C₇₃	—	2	1	no	—
466	Q₈×C₇₃	—	2	1	no	—
467	Q₈×C₇₃	—	2	1	no	—
468	Q₈×C₇₃	—	2	1	no	—
469	Q₈×C₇₃	—	4	2	no	—
470	Q₈×C₇₃	H(5,𝔽₂)	1	2	yes	—
471	D₄×C₇₃	—	2	1	no	—
472	D₄×C₇₃	—	2	1	no	—
473	D₄×C₇₃	—	8	1	no	—
474	C₂×C₄×C₇₃	—	2	1	no	—
475	C₂×C₄×C₇₃	—	2	2	no	—
476	C₂×C₄×C₇₃	—	2	1	no	—
477	C₂×C₄×C₇₃	—	2	1	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	2	1	no	—
480	C₂×C₄×C₇₃	—	2	1	no	—
481	C₂×C₄×C₇₃	—	2	1	no	—
482	C₂×C₄×C₇₃	—	2	1	no	—
483	C₂×C₄×C₇₃	—	2	1	no	—
484	C₂×C₄×C₇₃	—	4	1	no	—
485	C₂×C₄×C₇₃	—	4	2	no	—
486	C₂×C₄×C₇₃	—	4	2	no	—
487	C₂×C₄×C₇₃	—	8	1	no	—
488	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₇₃	—	2	4	no	—
495	C₂²⋊D₇₃	—	8	2	no	—
496	C₂²⋊D₇₃	—	8	2	no	—
497	C₂×Dic₇₃	—	2	2	no	—
498	C₂×Dic₇₃	—	2	2	no	—
499	C₂×Dic₇₃	—	2	2	no	—
500	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
501	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
502	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
503	D₂₉₂	—	2	2	no	—
504	D₂₉₂	—	2	2	no	—
505	D₂₉₂	—	4	4	no	—
506	D₂₉₂	—	4	2	no	—
507	D₂₉₂	—	8	1	no	—
508	D₂₉₂	#137	1	4	yes	complemented
509	C₄×D₇₃	—	2	4	no	—
510	C₄×D₇₃	—	2	2	no	—
511	C₄×D₇₃	—	2	2	no	—
512	C₄×D₇₃	—	4	2	no	—
513	C₄×D₇₃	—	4	4	no	—
514	C₄×D₇₃	—	8	2	no	—
515	C₄×D₇₃	—	8	2	no	—
516	C₄×D₇₃	—	8	2	no	—
517	C₄×D₇₃	—	8	2	no	—
518	Dic₁₄₆	—	2	2	no	—
519	Dic₁₄₆	—	2	2	no	—
520	Dic₁₄₆	—	2	2	no	—
521	Dic₁₄₆	—	2	2	no	—
522	Dic₁₄₆	—	2	2	no	—
523	Dic₁₄₆	—	4	4	no	—
524	Dic₁₄₆	—	8	2	no	—
525	Dic₁₄₆	—	8	2	no	—
526	Dic₁₄₆	—	8	1	no	—
527	C₈×C₇₃	—	2	1	no	—
528	C₈×C₇₃	—	2	1	no	—
529	C₈×C₇₃	—	2	1	no	—
530	C₈×C₇₃	—	2	1	no	—
531	#10596831	—	2	2	no	—
532	#10596831	—	2	2	no	—
533	C₂²×C₇₃	—	2	1	no	—
534	C₂²×C₇₃	—	2	1	no	—
535	C₂²×C₇₃	—	2	1	no	—
536	C₂²×C₇₃	—	4	1	no	—
537	C₂²×C₇₃	—	4	1	no	—
538	C₂²×C₇₃	—	4	1	no	—
539	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
540	C₂×D₇₃	—	2	2	no	—
541	C₂×D₇₃	—	2	2	no	—
542	C₂×D₇₃	—	4	2	no	—
543	C₂×D₇₃	—	4	2	no	—
544	C₂×D₇₃	—	4	2	no	—
545	C₂×D₇₃	—	16	4	no	—
546	C₂×D₇₃	C₂×#137	1	4	yes	—
547	C₄×C₇₃	—	2	1	no	—
548	C₄×C₇₃	—	2	1	no	—
549	C₄×C₇₃	—	2	2	no	—
550	C₄×C₇₃	—	2	1	no	—
551	C₄×C₇₃	—	2	1	no	—
552	C₄×C₇₃	—	4	1	no	—
553	C₄×C₇₃	—	4	1	no	—
554	C₄×C₇₃	—	4	1	no	—
555	C₄×C₇₃	—	4	1	no	—
556	C₄×C₇₃	—	4	1	no	—
557	C₄×C₇₃	—	4	1	no	—
558	C₄×C₇₃	C₂×#137	1	2	yes	—
559	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₄×C₇₃	#585	1	1	yes	characteristic
561	Dic₇₃	—	2	2	no	—
562	Dic₇₃	—	2	2	no	—
563	Dic₇₃	—	2	2	no	—
564	Dic₇₃	—	4	2	no	—
565	Dic₇₃	—	4	2	no	—
566	Dic₇₃	—	4	2	no	—
567	#61991	—	73	1	no	maximal, Sylow
568	C₂×C₇₃	—	4	1	no	—
569	C₂×C₇₃	—	8	1	no	—
570	C₂×C₇₃	#3488	1	1	yes	characteristic
571	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
572	C₂×C₇₃	#3584	1	1	yes	characteristic
573	D₇₃	—	2	4	no	—
574	D₇₃	—	8	2	no	—
575	#3514	—	73	1	no	—
576	Q₈×#41	—	73	1	no	—
577	#3400	—	73	1	no	—
578	#3398	—	73	1	no	—
579	#3375	—	73	1	no	—
580	#3369	—	73	1	no	—
581	#3316	—	73	2	no	—
582	#3314	—	73	2	no	—
583	#3299	—	73	1	no	—
584	#3295	—	73	1	no	—
585	D₄×Q₁₆	—	73	1	no	—
586	D₄×SD₁₆	—	73	1	no	—
587	#3270	—	73	2	no	—
588	#3266	—	73	2	no	—
589	#3252	—	73	1	no	—
590	#3248	—	73	2	no	—
591	#3215	—	73	2	no	—
592	#3210	—	73	1	no	—
593	#3117	—	73	2	no	—
594	#3108	D₇₃	1	1	yes	characteristic, complemented
595	#3037	—	73	1	no	—
596	C₂×#464	—	73	2	no	—
597	#2990	—	73	1	no	—
598	C₇₃	#61991	1	1	yes	characteristic, complemented, Sylow
599	C₂×#137	—	73	2	no	—
600	C₂²×Q₁₆	—	73	2	no	—
601	C₂²×SD₁₆	—	73	2	no	—
602	#559	—	73	1	no	—
603	Q₈²	—	73	1	no	—
604	#557	—	73	1	no	—
605	#557	—	146	1	no	—
606	#556	—	73	1	no	—
607	#555	—	146	1	no	—
608	#554	—	73	1	no	—
609	#554	—	73	2	no	—
610	#554	—	146	2	no	—
611	#554	—	146	1	no	—
612	#551	—	146	2	no	—
613	D₄×Q₈	—	73	2	no	—
614	D₄×Q₈	—	73	1	no	—
615	D₄×Q₈	—	73	1	no	—
616	#548	—	73	2	no	—
617	#546	—	73	2	no	—
618	#546	—	146	1	no	—
619	D₄²	—	73	1	no	—
620	#542	—	146	1	no	—
621	#538	—	146	2	no	—
622	#533	—	73	2	no	—
623	#533	—	73	1	no	—
624	#533	—	146	1	no	—
625	#533	—	146	2	no	—
626	#532	—	73	1	no	—
627	#529	—	73	2	no	—
628	#529	C₂×D₇₃	1	1	yes	characteristic
629	C₂×#124	—	73	2	no	—
630	#518	—	146	1	no	—
631	C₄×#41	—	73	1	no	—
632	C₄×#41	—	146	1	no	—
633	C₂×C₄×Q₈	—	73	2	no	—
634	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
635	#497	—	73	2	no	—
636	#497	—	73	2	no	—
637	#494	—	73	1	no	—
638	#492	—	73	1	no	—
639	#489	—	73	2	no	—
640	#489	—	73	2	no	—
641	#487	—	73	1	no	—
642	#486	—	73	1	no	—
643	#484	—	73	2	no	—
644	#483	C₂×D₇₃	1	1	yes	characteristic, complemented
645	#481	—	73	2	no	—
646	#480	C₂×D₇₃	1	1	yes	characteristic
647	#479	—	73	2	no	—
648	#479	C₂×D₇₃	1	1	yes	characteristic, complemented
649	#479	C₂×D₇₃	1	1	yes	characteristic, complemented
650	#477	—	73	1	no	—
651	#476	—	73	1	no	—
652	#475	—	73	2	no	—
653	#474	—	73	2	no	—
654	#470	—	73	2	no	—
655	#468	—	73	2	no	—
656	#467	—	73	2	no	—
657	#467	—	73	2	no	—
658	#465	—	73	2	no	—
659	#465	—	73	2	no	—
660	#464	—	73	2	no	—
661	#464	—	73	2	no	—
662	#464	—	73	2	no	—
663	#464	—	73	2	no	—
664	#464	—	73	2	no	—
665	#464	—	73	2	no	—
666	#464	—	73	2	no	—
667	#464	—	73	2	no	—
668	#464	—	73	2	no	—
669	#464	C₂×D₇₃	1	1	yes	characteristic
670	#464	C₂×D₇₃	1	1	yes	characteristic
671	#462	—	73	1	no	—
672	#462	—	73	1	no	—
673	#462	—	73	1	no	—
674	#462	—	73	2	no	—
675	#461	—	73	1	no	—
676	#461	—	73	2	no	—
677	#460	—	73	1	no	—
678	#460	—	73	1	no	—
679	#452	—	73	2	no	—
680	#452	—	73	2	no	—
681	#451	—	73	2	no	—
682	#451	—	73	2	no	—
683	#451	—	73	2	no	—
684	#451	C₂×D₇₃	1	1	yes	characteristic, complemented
685	#450	—	73	2	no	—
686	#450	—	73	2	no	—
687	#448	—	73	2	no	—
688	#448	C₂×D₇₃	1	1	yes	characteristic
689	#446	—	73	1	no	—
690	#446	—	73	1	no	—
691	#441	—	73	2	no	—
692	#441	—	73	2	no	—
693	#440	—	73	2	no	—
694	#440	—	73	2	no	—
695	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
696	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
697	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
698	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
699	#435	—	73	2	no	—
700	#435	—	73	2	no	—
701	C₈×D₄	—	73	1	no	—
702	C₈×D₄	—	73	1	no	—
703	#432	—	73	2	no	—
704	#431	C₂×D₇₃	1	1	yes	characteristic, complemented
705	#423	—	73	1	no	—
706	C₂×C₄⋊C₈	—	73	2	no	—
707	#417	—	73	2	no	—
708	C₂×#103	—	73	2	no	—
709	C₂×#102	—	73	2	no	—
710	C₂×#41	—	73	1	no	—
711	C₂×#41	—	73	2	no	—
712	C₂²×Q₈	—	73	2	no	—
713	C₂²×Q₈	—	73	2	no	—
714	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
715	C₂²×D₄	—	73	2	no	—
716	C₂²×D₄	—	146	1	no	—
717	#137	—	292	4	no	—
718	C₂×Q₁₆	—	292	4	no	—
719	C₂×Q₁₆	—	73	2	no	—
720	C₂×Q₁₆	—	73	2	no	—
721	C₂×Q₁₆	—	73	2	no	—
722	C₂×Q₁₆	—	73	2	no	—
723	C₂×Q₁₆	—	73	2	no	—
724	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
725	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
726	C₂×SD₁₆	—	292	4	no	—
727	C₂×SD₁₆	—	73	2	no	—
728	C₂×SD₁₆	—	73	2	no	—
729	C₂×SD₁₆	—	73	2	no	—
730	C₂×SD₁₆	—	73	2	no	—
731	C₂×SD₁₆	—	73	2	no	—
732	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
733	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
734	C₂×M₁₆	—	73	2	no	—
735	C₂²×C₈	—	73	2	no	—
736	C₂²×C₈	—	73	2	no	—
737	C₄⋊Q₈	—	73	2	no	—
738	C₄⋊Q₈	—	73	2	no	—
739	C₄⋊Q₈	—	73	1	no	—
740	C₄⋊Q₈	—	73	1	no	—
741	C₄⋊Q₈	—	73	1	no	—
742	C₄⋊Q₈	—	146	1	no	—
743	C₄⋊Q₈	—	146	1	no	—
744	C₄⋊Q₈	—	146	1	no	—
745	C₄⋊Q₈	—	146	2	no	—
746	C₄⋊Q₈	—	146	2	no	—
747	#127	—	73	1	no	—
748	#126	—	2	1	no	—
749	#126	—	146	2	no	—
750	#126	—	146	2	no	—
751	#125	—	146	1	no	—
752	#125	—	146	1	no	—
753	#125	—	146	2	no	—
754	#125	—	146	2	no	—
755	#125	—	146	2	no	—
756	#125	—	146	1	no	—
757	#125	C₂²×D₇₃	1	1	yes	characteristic
758	#124	—	73	2	no	—
759	#124	—	73	2	no	—
760	#124	—	73	2	no	—
761	#124	—	146	1	no	—
762	#124	—	146	2	no	—
763	#124	—	146	2	no	—
764	#124	—	146	2	no	—
765	#124	C₂²×D₇₃	1	1	yes	characteristic
766	#123	—	2	1	no	—
767	#123	—	146	2	no	—
768	#123	—	146	2	no	—
769	#123	—	146	2	no	—
770	C₂²⋊Q₈	—	73	2	no	—
771	C₂²⋊Q₈	—	73	2	no	—
772	C₂²⋊Q₈	—	73	2	no	—
773	C₂²⋊Q₈	—	73	2	no	—
774	C₂²⋊Q₈	—	146	2	no	—
775	C₂²⋊Q₈	—	146	2	no	—
776	C₂²⋊Q₈	—	146	2	no	—
777	C₂²⋊Q₈	—	146	2	no	—
778	C₂²⋊Q₈	—	146	2	no	—
779	C₂²⋊Q₈	—	146	2	no	—
780	C₂²⋊Q₈	—	146	2	no	—
781	C₂²⋊Q₈	—	146	2	no	—
782	C₂²⋊Q₈	—	146	2	no	—
783	C₂²⋊Q₈	—	146	1	no	—
784	C₂²⋊Q₈	—	146	1	no	—
785	C₂²⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
786	#121	—	73	2	no	—
787	#121	—	146	2	no	—
788	#121	—	146	2	no	—
789	#121	—	146	1	no	—
790	#121	—	146	1	no	—
791	#121	—	146	1	no	—
792	#121	C₂²×D₇₃	1	1	yes	characteristic
793	#120	—	146	2	no	—
794	#120	—	146	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	73	1	no	—
798	C₄×Q₈	—	73	1	no	—
799	C₄×Q₈	—	73	2	no	—
800	C₄×Q₈	—	73	2	no	—
801	C₄×Q₈	—	73	2	no	—
802	C₄×Q₈	—	73	2	no	—
803	C₄×Q₈	—	146	2	no	—
804	C₄×Q₈	—	146	2	no	—
805	C₄×Q₈	—	146	1	no	—
806	C₄×Q₈	—	146	1	no	—
807	C₄×Q₈	—	146	2	no	—
808	C₄×Q₈	—	146	1	no	—
809	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
810	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
811	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
812	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	73	2	no	—
816	C₄×D₄	—	73	2	no	—
817	C₄×D₄	—	73	2	no	—
818	C₄×D₄	—	73	1	no	—
819	C₄×D₄	—	73	1	no	—
820	C₄×D₄	—	146	1	no	—
821	C₄×D₄	—	146	1	no	—
822	C₄×D₄	—	146	1	no	—
823	C₄×D₄	—	146	1	no	—
824	C₄×D₄	—	146	2	no	—
825	C₄×D₄	—	146	2	no	—
826	C₄×D₄	—	146	2	no	—
827	C₄×D₄	—	146	2	no	—
828	C₄×D₄	—	146	1	no	—
829	C₄×D₄	—	146	1	no	—
830	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
831	#117	—	2	1	no	—
832	#117	—	73	1	no	—
833	#117	—	73	2	no	—
834	#117	—	146	2	no	—
835	#117	—	146	2	no	—
836	#117	—	146	1	no	—
837	#117	—	146	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	—	73	2	no	—
840	C₂×C₄⋊C₄	—	146	2	no	—
841	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
842	C₂×C₂²⋊C₄	—	146	2	no	—
843	C₂×C₂²⋊C₄	—	146	2	no	—
844	C₂×C₂²⋊C₄	—	146	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	73	2	no	—
847	C₂×C₄²	—	146	2	no	—
848	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
849	#107	—	73	2	no	—
850	#107	C₂²×D₇₃	1	1	yes	characteristic
851	#107	C₂²×D₇₃	1	1	yes	characteristic
852	#106	—	73	2	no	—
853	#106	C₂²×D₇₃	1	1	yes	characteristic
854	#106	C₂²×D₇₃	1	1	yes	characteristic
855	C₄⋊C₈	—	73	2	no	—
856	C₄⋊C₈	—	73	2	no	—
857	C₄⋊C₈	—	73	2	no	—
858	C₄⋊C₈	—	73	1	no	—
859	C₄⋊C₈	—	73	1	no	—
860	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
862	#103	—	73	2	no	—
863	#103	—	73	2	no	—
864	#103	—	73	2	no	—
865	#103	—	73	2	no	—
866	#103	—	73	2	no	—
867	#103	—	73	2	no	—
868	#103	—	73	2	no	—
869	#103	C₂²×D₇₃	1	1	yes	characteristic
870	#103	C₂²×D₇₃	1	1	yes	characteristic
871	#103	C₂²×D₇₃	1	1	yes	characteristic
872	#103	C₂²×D₇₃	1	1	yes	characteristic
873	#103	C₂²×D₇₃	1	1	yes	characteristic
874	#103	C₂²×D₇₃	1	1	yes	characteristic
875	#102	—	73	2	no	—
876	#102	—	73	2	no	—
877	#102	—	73	2	no	—
878	#102	—	73	2	no	—
879	#102	—	73	2	no	—
880	#102	C₂²×D₇₃	1	1	yes	characteristic
881	#102	C₂²×D₇₃	1	1	yes	characteristic
882	C₂²⋊C₈	—	73	2	no	—
883	C₂²⋊C₈	—	73	2	no	—
884	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
885	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
886	#97	—	73	2	no	—
887	#97	—	73	2	no	—
888	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
889	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
890	C₂⁴	—	146	2	no	—
891	#41	—	292	2	no	—
892	#41	—	292	2	no	—
893	#41	—	146	4	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	4	1	no	—
897	C₂×Q₈	—	292	2	no	—
898	C₂×Q₈	—	292	2	no	—
899	C₂×Q₈	—	292	2	no	—
900	C₂×Q₈	—	73	1	no	—
901	C₂×Q₈	—	73	2	no	—
902	C₂×Q₈	—	73	2	no	—
903	C₂×Q₈	—	146	2	no	—
904	C₂×Q₈	—	146	2	no	—
905	C₂×Q₈	—	146	2	no	—
906	C₂×Q₈	—	146	4	no	—
907	C₂×Q₈	—	146	1	no	—
908	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
909	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
910	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	292	4	no	—
913	C₂×D₄	—	292	2	no	—
914	C₂×D₄	—	292	2	no	—
915	C₂×D₄	—	73	2	no	—
916	C₂×D₄	—	73	1	no	—
917	C₂×D₄	—	73	2	no	—
918	C₂×D₄	—	146	2	no	—
919	C₂×D₄	—	146	2	no	—
920	C₂×D₄	—	146	2	no	—
921	C₂×D₄	—	146	1	no	—
922	C₂×D₄	—	146	1	no	—
923	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	73	2	no	—
928	C₂²×C₄	—	73	2	no	—
929	C₂²×C₄	—	73	2	no	—
930	C₂²×C₄	—	146	2	no	—
931	C₂²×C₄	—	146	2	no	—
932	C₂²×C₄	—	146	2	no	—
933	C₂²×C₄	—	146	2	no	—
934	C₂²×C₄	—	146	2	no	—
935	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
936	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
937	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
938	Q₁₆	—	2	2	no	—
939	Q₁₆	—	4	1	no	—
940	Q₁₆	—	292	2	no	—
941	Q₁₆	—	292	2	no	—
942	Q₁₆	—	292	2	no	—
943	Q₁₆	—	292	2	no	—
944	Q₁₆	—	146	4	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	4	1	no	—
947	SD₁₆	—	292	2	no	—
948	SD₁₆	—	292	2	no	—
949	SD₁₆	—	292	2	no	—
950	SD₁₆	—	292	2	no	—
951	SD₁₆	—	146	4	no	—
952	M₁₆	—	292	2	no	—
953	C₂×C₈	—	292	2	no	—
954	C₂×C₈	—	292	2	no	—
955	C₂×C₈	—	73	2	no	—
956	C₂×C₈	—	73	2	no	—
957	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
958	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
959	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	73	2	no	—
971	C₄⋊C₄	—	73	2	no	—
972	C₄⋊C₄	—	73	1	no	—
973	C₄⋊C₄	—	73	1	no	—
974	C₄⋊C₄	—	73	2	no	—
975	C₄⋊C₄	—	146	2	no	—
976	C₄⋊C₄	—	146	2	no	—
977	C₄⋊C₄	—	146	2	no	—
978	C₄⋊C₄	—	146	2	no	—
979	C₄⋊C₄	—	146	2	no	—
980	C₄⋊C₄	—	146	2	no	—
981	C₄⋊C₄	—	146	2	no	—
982	C₄⋊C₄	—	146	2	no	—
983	C₄⋊C₄	—	146	2	no	—
984	C₄⋊C₄	—	146	2	no	—
985	C₄⋊C₄	—	146	2	no	—
986	C₄⋊C₄	—	146	2	no	—
987	C₄⋊C₄	—	146	1	no	—
988	C₄⋊C₄	—	146	1	no	—
989	C₄⋊C₄	—	146	1	no	—
990	C₄⋊C₄	—	146	1	no	—
991	C₄⋊C₄	—	146	1	no	—
992	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	73	2	no	—
1002	C₂²⋊C₄	—	73	2	no	—
1003	C₂²⋊C₄	—	73	2	no	—
1004	C₂²⋊C₄	—	146	2	no	—
1005	C₂²⋊C₄	—	146	2	no	—
1006	C₂²⋊C₄	—	146	2	no	—
1007	C₂²⋊C₄	—	146	2	no	—
1008	C₂²⋊C₄	—	146	2	no	—
1009	C₂²⋊C₄	—	146	2	no	—
1010	C₂²⋊C₄	—	146	2	no	—
1011	C₂²⋊C₄	—	146	2	no	—
1012	C₂²⋊C₄	—	146	2	no	—
1013	C₂²⋊C₄	—	146	2	no	—
1014	C₂²⋊C₄	—	146	2	no	—
1015	C₂²⋊C₄	—	146	2	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	73	2	no	—
1022	C₄²	—	73	2	no	—
1023	C₄²	—	73	2	no	—
1024	C₄²	—	146	2	no	—
1025	C₄²	—	146	2	no	—
1026	C₄²	—	146	2	no	—
1027	C₄²	—	146	2	no	—
1028	C₄²	D₄×D₇₃	1	1	yes	characteristic
1029	C₄²	D₄×D₇₃	1	1	yes	characteristic
1030	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1031	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1032	C₂³	—	2	1	no	—
1033	C₂³	—	292	4	no	—
1034	C₂³	—	584	2	no	—
1035	C₂³	—	584	2	no	—
1036	C₂³	—	73	2	no	—
1037	C₂³	—	146	2	no	—
1038	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	292	4	no	—
1046	Q₈	—	584	1	no	—
1047	Q₈	—	584	2	no	—
1048	Q₈	—	584	2	no	—
1049	Q₈	—	146	2	no	—
1050	Q₈	—	146	2	no	—
1051	Q₈	—	146	2	no	—
1052	Q₈	—	146	2	no	—
1053	Q₈	—	146	2	no	—
1054	Q₈	#14556637	1	2	yes	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	292	4	no	—
1059	D₄	—	292	2	no	—
1060	D₄	—	584	1	no	—
1061	D₄	—	584	2	no	—
1062	D₄	—	584	2	no	—
1063	D₄	—	73	4	no	—
1064	D₄	—	146	4	no	—
1065	D₄	—	146	2	no	—
1066	D₄	—	146	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	4	1	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	292	4	no	—
1082	C₂×C₄	—	292	2	no	—
1083	C₂×C₄	—	584	2	no	—
1084	C₂×C₄	—	584	2	no	—
1085	C₂×C₄	—	584	2	no	—
1086	C₂×C₄	—	584	2	no	—
1087	C₂×C₄	—	73	2	no	—
1088	C₂×C₄	—	73	2	no	—
1089	C₂×C₄	—	73	2	no	—
1090	C₂×C₄	—	146	4	no	—
1091	C₂×C₄	—	146	2	no	—
1092	C₂×C₄	—	146	2	no	—
1093	C₂×C₄	—	146	2	no	—
1094	C₂×C₄	—	146	2	no	—
1095	C₂×C₄	—	146	2	no	—
1096	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1097	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1098	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1099	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1100	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1101	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	146	2	no	—
1107	C₈	—	146	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	292	2	no	—
1115	C₂²	—	292	2	no	—
1116	C₂²	—	292	2	no	—
1117	C₂²	—	73	4	no	—
1118	C₂²	—	1168	4	no	—
1119	C₂²	—	146	2	no	—
1120	C₂²	—	146	2	no	—
1121	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	292	2	no	—
1134	C₄	—	292	2	no	—
1135	C₄	—	292	2	no	—
1136	C₄	—	146	2	no	—
1137	C₄	—	146	2	no	—
1138	C₄	—	146	2	no	—
1139	C₄	#137×D₇₃	1	2	yes	—
1140	C₄	C₂×#14556637	1	1	yes	characteristic
1141	C₄	#17989423	1	1	yes	characteristic
1142	C₂	—	4	1	no	—
1143	C₂	—	8	1	no	—
1144	C₂	—	584	2	no	—
1145	C₂	—	146	4	no	—
1146	C₂	#22623592	1	1	yes	characteristic
1147	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1148	C₂	#22624700	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3108	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#22623894	C₂
hypercenter	#3108	D₇₃
hypocenter	C₇₃	#61991
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3108

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. Q₈×#11924028	C₂	semidirect
3. #22622982	C₂	semidirect
4. #22622960	C₂	semidirect
5. #22622743	C₂	semidirect
6. #22622669	C₂	semidirect
7. #22622045	C₂	semidirect
8. #22622015	C₂	semidirect
9. #22621809	C₂	semidirect
10. #22621757	C₂	semidirect
11. Q₁₆×D₂₉₂	C₂	semidirect
12. SD₁₆×D₂₉₂	C₂	semidirect
13. #22621504	C₂	semidirect
14. #22621444	C₂	semidirect
15. #22621304	C₂	semidirect
16. #22621267	C₂	semidirect
17. #22620932	C₂	semidirect
18. #22620889	C₂	semidirect
19. #22620107	C₂	semidirect
20. #22619403	C₂	semidirect
21. #464×D₇₃	C₂	semidirect
22. #22619052	C₂	semidirect
23. C₇₃×#3108	C₂	semidirect
24. C₂×#14556622	C₂²	semidirect
25. C₂×Q₁₆×D₇₃	C₂²	semidirect
28. Q₈×Dic₁₄₆	C₂²	semidirect
30. #17989315	C₂²	semidirect
36. #17989292	C₂²	semidirect
40. Q₈×C₂²⋊D₇₃	C₂²	semidirect
48. #17989144	C₂²	semidirect
50. #17989141	C₂²	semidirect
57. C₄×Q₈×D₇₃	C₂²	semidirect
58. #17988980	C₂²	semidirect
60. #17988967	C₂²	semidirect
62. #17988948	C₂²	semidirect
64. #17988938	C₂²	semidirect
66. #17988924	C₂²	semidirect
68. #17988891	C₂²	semidirect
69. #17988882	C₂²	semidirect
71. #17988871	C₂²	semidirect
72. #17988866	C₂²	semidirect
73. #17988843	C₂²	semidirect
75. #17988829	C₂²	semidirect
76. #17988827	C₂²	semidirect
79. #17988812	C₂²	semidirect
80. #17988811	C₂²	semidirect
81. #17988810	C₂²	semidirect
82. #17988810	C₂²	semidirect
83. #17988809	C₂²	semidirect
84. #17988809	C₂²	semidirect
88. #17988797	C₂²	semidirect
89. #17988797	C₂²	semidirect
90. #17988797	C₂²	semidirect
91. #17988796	C₂²	semidirect
93. #17988791	C₂²	semidirect
96. #17988751	C₂²	semidirect
97. #17988751	C₂²	semidirect
98. #17988744	C₂²	semidirect
99. #17988744	C₂²	semidirect
100. #17988741	C₂²	semidirect
104. #17988717	C₂²	semidirect
105. #17988717	C₂²	semidirect
106. #17988693	C₂²	semidirect
107. #17988691	C₂²	semidirect
108. #17988690	C₂²	semidirect
109. #17988686	C₂²	semidirect
110. #17988661	C₂²	semidirect
111. #17988661	C₂²	semidirect
114. #17988643	C₂²	semidirect
115. #17988611	C₂²	semidirect
116. C₄⋊C₈×D₇₃	C₂²	semidirect
117. #17988586	C₂²	semidirect
118. #103×D₇₃	C₂²	semidirect
121. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
122. #483×C₇₃	C₂²	semidirect
124. #479×C₇₃	C₂²	semidirect
125. #479×C₇₃	C₂²	semidirect
128. #451×C₇₃	C₂²	semidirect
130. C₄×Q₁₆×C₇₃	C₂²	semidirect
131. C₄×Q₁₆×C₇₃	C₂²	semidirect
134. #431×C₇₃	C₂²	semidirect
508. D₂₉₂	#137	semidirect
594. #3108	D₇₃	semidirect
598. C₇₃	#61991	semidirect
634. C₂×C₄×Q₈	C₂×D₇₃	semidirect
644. #483	C₂×D₇₃	semidirect
648. #479	C₂×D₇₃	semidirect
649. #479	C₂×D₇₃	semidirect
684. #451	C₂×D₇₃	semidirect
695. C₄×Q₁₆	C₂×D₇₃	semidirect
696. C₄×Q₁₆	C₂×D₇₃	semidirect
704. #431	C₂×D₇₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22623894	2
Q₈×#11924028	2
#22622982	2
#22622960	2
#22622743	2
#22622669	2
#22622045	2
#22622015	2
#22621809	2
#22621757	2
Q₁₆×D₂₉₂	2
SD₁₆×D₂₉₂	2
#22621504	2
#22621444	2
#22621304	2
#22621267	2
#22620932	2
#22620889	2
#22620107	2
#22619403	2
#464×D₇₃	2
#22619052	2
C₇₃×#3108	2
#61991	73